**End behavior of graph functions** are as important as its conceptualization. It is very important for every function to exhibit the right behavior. Graph functions that do not exhibit the right behavior are very dangerous and can cause severe problems for the user and also for the performance of the system. It is very important for the designer to check out the behavior of the graph before it gets implemented in any system. There are certain points to be kept in mind while performing this test.

The first and most important thing that one needs to see in the **end behavior of the graph** is whether it exhibits steady state behavior or random state behavior. There are some functions which change their behavior depending upon the values set as part of their initialization. For such functions the graph designer can make some changes in the initialization, set up of data fields etc. in order to make the graph behave in the desired manner.

Another important thing that is to be checked for is the over-or underflow behavior of the functions. This happens when more value is added than the required value. Overflow behavior occurs when the value gets more than the end value. Underflow behavior occurs when the value is less than the end value. Graph design with appropriate functions can bring out interesting and successful results.

Any chart that contains a trend line can be analyzed using the graphing techniques for end behavior. It is necessary to analyze the trends for the graph to be effective and useful. It is advisable to create a range histogram and a time series plot in order to check the trends of the functions. This can be done in different ways.

A simple method for end behavior checking is to plot a line through the points as the range histogram will show. When the line separates two ranges, it indicates that the range is more or less separated. When the line does not separate the ranges, the range is too wide. This clearly shows that the data has no significant trends. It is better to make an averag**e** calculation and average the results than to plot a line through the points.

**Analyzing the end behavior of the graphs** is very important. The analysis can be done by many different methods including mathematical calculations or by looking at the behavior of the functions themselves. Most of the analysis is carried out by the function creators themselves. The visualization of the end behavior of the function helps in getting a better understanding of the way the graph functions behave. This helps the creators understand the various concepts of the graph design.

## Behaviors of an End Behavior of Graph Functions

The end behavior of Graph functions is a matter of great interest to me. Let me tell you first why I am interested in this subject, and how I have benefited from it, both personally and professionally. You see, I used to be a property & land developer in the late 80’s, and I loved to build all types of structures (both residential and commercial) over a period of about 5 years.

When I looked back at what I had done, it seemed to me that what I was doing was a very “personal” way of getting my point across to the potential buyers of the properties I was selling. As I looked back at the graph I had created during those days in those projects, and compared it to the sales contracts I had given to the customers, I could see that I had indeed communicated my ideas more effectively through graphs than I would have done so otherwise.

In other words, my end behavior of graph functions was clearly geared at communicating the “point” I was trying to make, in a language that everyone in the project could understand. I think the lesson here was that if you truly want to get your point across, and you can do so effectively through a graph, then by all means stick with a graph.

The other interesting topic is that the same Graph function behaves differently when it is being used in different applications. For example, when you look at a “time series” like I showed above, the end behavior of a graph function varies depending on the application. In this case, you want to create a zero degree curve. This means that for any x in the data, the slope of the line going across the graph would be exactly zero. In other cases, the graph will behave more aggressively, graphing a steep “U-shape” as the data range crosses the x-axis.